Post on 14-May-2020
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An Analysis of Einstein’s Second Postulate
to his Special Theory of Relativity
Edward G. Lake* Independent Researcher
(Dated: April 20, 2017)
Abstract: An analysis of books, presentations and scientific papers about Albert
Einstein’s Second Postulate to his Special Theory of Relativity shows that there is a
fundamental disagreement between what Einstein wrote and how what he wrote is being
interpreted by mathematician-physicists and taught in colleges and universities around
the world. An analysis of the evidence shows that Einstein was correct and the
interpretations and teachings are incorrect.
*sole author
ORCID ID: 0000-0002-4933-2714
Key words: physics, relativity, second postulate, time dilation, time, speed of light
Email: detect@outlook.com
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Einstein’s 1905 paper On the Electrodynamics of Moving Bodies [1] begins with a
description of certain “asymmetries” regarding how magnets and conductors appear to work
when one is moving while the other is “at rest.” Then, while still on page 1, Einstein wrote:
“Examples of this sort, together with the unsuccessful attempts to discover any motion of
the earth relatively to the “light medium,” suggest that the phenomena of electrodynamics as well
as of mechanics possess no properties corresponding to the idea of absolute rest. They suggest
rather that, as has already been shown to the first order of small quantities, the same laws of
electrodynamics and optics will be valid for all frames of reference for which the equations
of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be
called the “Principle of Relativity”) to the status of a postulate, and also introduce another postulate,
which is only apparently irreconcilable with the former, namely, that light is always propagated in
empty space with a definite velocity c which is independent of the state of motion of the
emitting body. These two postulates suffice for the attainment of a simple and consistent theory of
the electrodynamics of moving bodies based on Maxwell’s theory for stationary bodies.”
The first postulate is, therefore, “the same laws of electrodynamics and optics will be
valid for all frames of reference for which the equations of mechanics hold good.” In other
words, regardless of the speed or direction you may be moving, if you are “at rest” in your
frame of reference (i.e., if you are stationary or moving at a constant rate along with everything
used as a reference), the same mathematical equations using the same laws of electrodynamics
and optics will produce the same valid results as in any other frame of reference that is similarly
“at rest.” This is the “Principle of Relativity” and primarily relates to Time Dilation, where Time
may pass at a different rate within each “frame of reference” while appearing perfectly
“normal” to each observer in each frame of reference.
For example, a scientist in a lab in Colorado can set up equipment to measure the speed
of light. The equipment consists of a light pulse emitter and detector at one end of the inside
of a long vacuum chamber, a mirror exactly two meters away at the other end of the vacuum
chamber, and an atomic clock to keep track of time. A light pulse is emitted toward the mirror,
it “bounces off” the mirror, and it hits the detector next to the emitter. The atomic clock
measures the time between emission and detection. The results of the experiment would show
that the speed of light is 299,792,458 meters per local second as measured by the atomic clock.
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Figure 1
Meanwhile, an astronaut-scientist aboard a space ship traveling at a constant speed of
5% of the speed of light can set up exactly the same equipment, and he will also measure the
speed of light to be 299,792,458 meters per his local second according to his atomic clock.
Figure 2
Due to velocity Time Dilation, a “local second” has a different length for the scientist in
Colorado versus the astronaut scientist. One second will pass for the scientist in Colorado
while, due to his speed and velocity Time Dilation, approximately 1.00125 seconds pass for the
astronaut-scientist. But, as long as they do not make any comparisons, they will not notice any
difference because the “same laws of electrodynamics and optics” apply in each location, and
the fact that the length of a second is a variable has no effect on the “equations of mechanics.”
The astronaut-scientist can set up the equipment with the vacuum chamber aligned
with the space ship’s direction of motion or perpendicular to the ship’s direction of motion, and
the results will be the same, just as they were for Michelson and Morley.[2]
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Figure 3
Such tests would confirm that the laws of electrodynamics and optics work the same in
both frames of reference, as do the mathematical equations involved. The change in the length
of a second due to velocity Time Dilation doesn’t affect the electrodynamics, the optics or the
equations. Nor does the direction of motion. All in accordance with Einstein’s First Postulate.
The conflicting interpretations of the Second Postulate are the focus of this paper. Once
again, the Second Postulate is: “light is always propagated in empty space with a definite
velocity c which is independent of the state of motion of the emitting body.”
The astronaut scientist on that space ship traveling at 5% of the speed of light has
measured the speed of light to be 299,792,458 meters per his local second. If he opens the
mirror end of the chamber, he can be certain that the photons exiting the chamber in the same
direction the space ship is moving will be traveling at 299,792,458 meters per his local second.
Figure 4
If he opens the detector end of the chamber, he can be equally certain that the photons
exiting the chamber in the direction opposite to the direction the ship is moving will also be
traveling at 299,792,458 meters per his local second.
Figure 5
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The motion of the emitting body did not and cannot combine with the speed of light
being emitted. That is all the Second Postulate says. When a photon of light is emitted by an
atom, it is isotropic, which means it has the same properties regardless of the direction it
travels. It also travels at the local speed of light regardless of how the emitter is moving.
When Einstein wrote that the Second Postulate “is only apparently irreconcilable with”
the First Postulate, he seems to have been referring to the fact that while the observer standing
next to the emitter measures light he emits as moving at a speed that is independent of his
own speed, that fact does not apply to light he may measure coming from another source
outside of his frame of reference. Light coming from another source can arrive at c + or – v,
where v is his own velocity. Some may interpret that to mean that different laws of
electrodynamics and optics apply to the light from the other source. According to Einstein,
such an interpretation would be incorrect. Light that is emitted by a moving emitter will travel
at the speed of light as it exists at the source of the light, and light coming from another source
(in another “frame of reference”) will travel at the speed of light as it exists at its source. The
same “equations of mechanics hold good” for both emitters of light.
The implication is that there is a natural or physical limit on how fast light can be
emitted. That limit is 299,792,458 meters per second at the location of the emitter. But there
is nothing to prevent any observer from measuring the speed of light coming from some other
source to be c + or - his own velocity, since that would have nothing to do with the natural or
physical limit on the speed of the light that was emitted. It is just mathematics.
For the purposes of this paper, I’ll call the above interpretation of Einstein’s First and
Second Postulates “Einstein’s Emitter Only Theory.” Once it is accepted that Time can move at
different rates in different frames of reference, the above interpretation is perfectly logical and
fully compatible with common sense.
Einstein was well aware that mathematicians and Quantum Mechanics did not agree
with his theory. He famously said, “Since the mathematicians have invaded the theory of
relativity I do not understand it myself anymore.”[3] And, “As far as the laws of mathematics
refer to reality, they are not certain, and as far as they are certain, they do not refer to
reality.”[4] Einstein went to his grave arguing with mathematicians.
Here is American mathematical physicist Richard C. Tolman’s interpretation of the
second postulate from a scientific paper he published in 1910:
The second postulate of relativity is obtained by a combination of the first postulate with a
principle which has long been familiar in the theory of light. This principle states that the velocity of
light is unaffected by a motion of the emitting source, in other words, that the velocity with which
light travels past any observer is not increased by a motion of the source of light towards the
observer. The first postulate of relativity adds the idea that a motion of the source of light towards
the observer is identical with a motion of the observer towards the source. The second postulate
of relativity is seen to be merely the combination of these two principles, since it states that
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the velocity of light in free space appears the same to all observers regardless both of the
motion of the source of light and of the observer.[5]
Here is an interpretation of the Second Postulate as printed in 2012 in the ninth edition
of a widely used college text book:
In 1905 Albert Einstein proposed a theory that explained the result of the Michelson–
Morley experiment and completely altered our notions of space and time. He based his special
theory of relativity on two postulates:
1. The principle of relativity: All the laws of physics are the same in all inertial frames.
2. The constancy of the speed of light: The speed of light in a vacuum has the same value,
c = 2.997 924 58 x 108 m/s, in all inertial reference frames, regardless of the velocity of the
observer or the velocity of the source emitting the light.[6]
A little research will find other college text books with minor variations on that same
wording. Examples:
“Second postulate: The speed of light in a vacuum is constant and will have the same
value for all observers independent of their motion relative to the light source.”[7]
“The unusual properties of the velocity of light are: It is a constant for all observers,
irrespective of how they are moving. It is a universal speed limit, which no material object can
exceed. It is independent of the velocity of its source and that of the observer.”[8]
“Einstein concluded by 1905 that Maxwell's theory must be reinterpreted: the speed of
light will be exactly the same – a universal constant - for all observers, no matter whether they
move (with constant velocity) relative to the source of the light. This highly original insight became
Einstein's second postulate of relativity, the Principle of the Consistency of the Speed of Light:
“Light and all other forms of electromagnetic radiation are propagated in empty
space with a constant velocity c which is independent of the motion of the observer
or the emitting body.
“Einstein is saying that, whether moving at uniform speed toward or away from the
source of light or alongside the emitted light beam, any observer always measures the
exact same value for the speed of light in a vacuum, which is about 3.0 x 108 m/s or
300,000 km/s (186,000 mi/s).”[9]
There are a great many scientific papers and many other books which describe the
second postulate the same way.
I will call this interpretation the “Mathematicians’ All Observers Theory.”
I can only speculate as to exactly how and why the “Mathematicians’ All Observers
Theory” was developed. In some situations, it appears to be the result of simply
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misinterpreting Einstein’s two postulates. In other situations, it appears to be the result of a
refusal to accept Einstein’s views about Time and Time Dilation.
Before the Space Age and the invention of atomic clocks it was difficult to prove the
mathematicians wrong. Even today there is no precise way for anyone to measure the speed of
light emitted by some distant source such as a star. To detect a photon is to destroy the
photon. Therefore, there is no way to detect a photon as it enters a chamber of specified
length and then detect it again when it hits the far end of the chamber.
Research to locate experiments which the “Mathematicians’ All Observers” theorists use
to argue confirmation of their theory that light always travels at the same speed for all
observers found two primary experiments which those theorists claim does so.
The first experiment was performed by T. Alväger et. al in 1964.[10] Alväger et al
measured the speed of gamma rays emitted by a beam of pions moving at almost the speed of
light with respect to their laboratory. They found that the speed of the light emitted by the
moving sources was the same as light emitted by sources “at rest” in the laboratory. In other
words, there was no moving observer involved. All they did was confirm that the speed of
light emitted from pions while moving at nearly the speed of light was the same as the speed of
light measured under standard conditions in the same laboratory. They proved what Einstein
wrote: “light is always propagated in empty space with a definite velocity c which is
independent of the state of motion of the emitting body.” They didn’t prove anything about
what a moving observer might see and measure.
The second experiment was performed in 2011 by E. B. Aleksandrov et al.[11] They did
basically the same thing; they measured “the velocity of the light pulse emitted by an
ultrarelativistic electron bunch.” They determined that the speed of light was not affected by
the speed of the “ultrarelativistic electron bunch.” There was no moving observer involved.
The theoreticians who advocate the “Mathematician’s All Observers Theory” also cite
various experiments by different labs which demonstrate that light is isotropic, i.e., that light
travels at the same velocity in all directions. Again, it has absolutely nothing to do with
demonstrating that light will somehow adjust to the speed of all oncoming observers to allow
them to measure the light at 299,792,458 meters per second regardless of their own motion. It
merely confirms that when an atom generates a photon, that photon is emitted instantly.
Therefore the speed of the emitted photon is unaffected by any directional momentum which
may be affecting the atom itself.
Meanwhile, there have been countless “experiments” which demonstrate that the
“Einstein’s Emitter Only Theory” is correct while at the same time showing that the
“Mathematicians’ All Observers Theory” is incorrect. But there are few scientific papers about
them.
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The Lunar Laser Ranging Experiment
A search to find published (or unpublished) scientific papers which disprove the
“Mathematicians’ all observers” version of the Second Postulate found only one such paper.
NASA has performed some experiments in which they bounced laser light pulses off of
reflectors left on the moon by the Apollo 14 and Apollo 15 manned missions to the moon. An
experiment in 2009 demonstrated a way to precisely measure the speed of incoming light in an
indirect way – by timing pulses. The experiment confirmed that the velocity of the observer
will be added to the oncoming speed of light when the observer is traveling toward the source
of the light. I.e., they confirmed “Einstein’s Emitter Only Theory” and disproved the
“Mathematicians’ All Observer Theory.” But, amazingly, they did not accept what they had
confirmed.
The paper is titled “Lunar Laser Ranging Test of the Invariance of c.”[13] It was written
by a NASA scientist, Daniel Y. Gezari, who made the paper public via Cornell University and their
ArXiv.org library web site. The abstract reads as follows:
The speed of laser light pulses launched from Earth and returned by a retro-
reflector on the Moon was calculated from precision round-trip time-of-flight
measurements and modeled distances. The measured speed of light (c) in the moving
observer’s rest frame was found to exceed the canonical value c = 299,792,458 m/s by
200±10 m/s, just the speed of the observatory along the line-of-sight due to the
rotation of the Earth during the measurements. This result is a first-order violation of
local Lorentz invariance; the speed of light seems to depend on the motion of the
observer after all, as in classical wave theory, which implies that a preferred reference
frame exists for the propagation of light. However, the present experiment cannot
identify the physical system to which such a preferred frame might be tied.
In other words, NASA scientists emitted a pulse of photons from a point on earth,
bounced those photons off a reflector on the moon, and then recorded the photons’ arrival
time at that same point on earth. The results showed that light either traveled faster than the
speed of light or the movement of the earth during the round trip had to be added to the speed
of light in direct violation of the “Mathematicians’ All Observer” interpretations of Einstein’s
Second Postulate.
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Figure 6
The experiment was basically very simple (although in practice it is incredibly complex).
The reflector left on the moon bounced any light emitted directly toward it directly back toward
the light source. The light source used by NASA in this instance was a laser at their Apache
Point Observatory in New Mexico. The reflector was the one left on the moon by the Apollo 15
mission.
The travel time for the light would therefore be calculated using the distance from the
transmitter to the reflector and back again to the detector located next to the emitter. This is
very similar to the way light is typically measured in laboratories on Earth, with two major
differences: (1) The distance between the emission point and the mirror is much greater, and
(2) the Earth is spinning on its axis, and the emitter and detector were therefore moving toward
the reflector. (The moon is also moving, but its movement is negligible compared to the
rotation speed of the Earth.)
Here’s a simplified step by step description of what happened. In the line of dots below,
E represents the Earth and M represents the Moon at the time a laser beam is fired from E
toward M.
E…………………………………………………………………………………..………………………………………M
According to those who believe that the “Speed of light is same for all observers
regardless of their state of motion with respect to source,” light will always travel at the same
speed when going from E to M or from M to E regardless of any movement by E or M.
In reality, however, “light is always propagated in empty space with a definite velocity c
which is independent of the state of motion of the emitting body.” And that only means that
when light is emitted from E (the Earth) toward M (the moon), the motion of the Earth does not
affect the speed of light. Light travels at 299,892,458 meters per second regardless of how fast
the Earth was moving or in what direction at the time of emission.
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However, the movement of the Earth while the pulse of light is traveling to and from the
moon requires that the line of dots should look like those below.
E….A...B…………………………………………………………………………………………………………………M
A laser pulse of light is fired from E toward M at 299,892,458 meters per second.
While the pulse of light was traveling toward the reflector on the moon, the Earth
moved from position E to position A.
The photons hit the reflector at M when the Earth was at position A. New photons were
emitted by the atoms in the reflector and directed toward the Earth.
While the photons were traveling from the reflector on the moon towards the detector
on Earth, the Earth moved from position A to position B.
The photons hit the detector when the Earth was at position B.
The motion of the Earth did not affect the actual speed of light, of course, but it did
affect the distance the light had to travel to complete the experiment. Therefore, the observer
at the Apache Point Observatory who believed that the speed of light is the same for all
observers calculated the incoming light was traveling at the speed of light plus the speed of the
observatory, “a first-order violation of local Lorentz invariance,” i.e., an “impossibility.”
The paper by Gezari is an attempt to figure out how this apparent “impossibility” can
happen. The author suggests “a preferred reference frame exists for the propagation of light.”
But he couldn’t figure out how it works, so he wrote, “However, the present experiment cannot
identify the physical system to which such a preferred frame might be tied.”
If you do not misinterpret the Second Postulate, of course, you do not need a “preferred
reference frame,” and everything worked just as you would expect it to work.
Plus, the Lunar Laser Ranging experiments suggest more ways to further verify that the
motion of an independent observer will combine with the velocity of incoming light, i.e., that
light will not somehow magically slow down to compensate for the observer’s velocity.
The Lunar Laser Ranging experiments were able to measure the speed of the incoming
light because the light was emitted in timed pulses. They knew when the pulse of laser light
was emitted, so they knew the exact time when they would expect the reflected light pulse to
return. If they had emitted a constant stream of photons, they wouldn’t have been able to time
any specific photon. If they had a light transmitter on the moon that emitted a very short pulse
of light every second, however, they would have observed the same anomaly. In such a
situation, when the observer on the Earth was moving toward the moon, the pulses would have
come faster than one per second, which would be misinterpreted as indicating the light was
traveling faster than the speed of light.
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So, we have what seems to be a very important key to resolving the disputes over the
Second Postulate. The two different interpretations can be proved or disproved by an
experiment which involves the emission of light or energy waves in discrete evenly timed pulses
and the measuring of those waves by a moving outside observer. Fortunately, that kind of
“experiment” is performed every day by police officers around the world.
Laser “speed guns”
During the past couple decades, police departments around the world have been
gradually implementing the use of laser speed guns to catch violators of local speed laws –
replacing the older radar guns. The technique is referred to as “lidar” (LIght Detection And
Ranging). Lidar guns use light pulses to determine the speed at which a vehicle is traveling. The
technique directly relates to the Lunar Laser Ranging Experiment and easily demonstrates
which Second Postulate interpretation is correct. All we have to do is set up an “experiment”
that is the same as police officers perform every day. All we need is a speeder moving at 90
miles per hour toward a stationary police car which has a lidar gun pointed at the speeder – and
an understanding of exactly what steps take place in the “experiment.”
Figure 7
Step 1: The lidar gun is the emitter. The stationary lidar gun in the stationary police car
emits very short pulses of laser light – a small fraction of a second apart - toward the speeder.
The police car is stationary and the pulses, of course, move at c, the speed of light. To simplify
things for purposes of this “experiment,” we can assume each pulse consists of one photon.
Step 2: The speeder starts out as an observer. As he moves toward the emitter, the
first photon hits an atom in his vehicle, arriving at c + v.
Step 3: An atom in the surface of the speeder’s vehicle absorbs the light energy from
the first photon.
Step 4: Unable to hold the excess energy it absorbed, the atom immediately emits a
new photon out again, back in the direction of the police car.
Step 5: The speeder’s car moves forward slightly as the second photon approaches.
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Step 6: The second photon comprising the second pulse from the lidar gun hits another
atom in the surface of the speeder’s vehicle, again arriving at c + v.
Step 7: Unable to hold the excess energy it absorbed, the second atom immediately
emits a new photon out again, back in the direction of the police car.
Note: The speeder is an observer when the light is coming to him, and he becomes an
emitter when sending the light back to the lidar gun in the police car. As stated in “Einstein’s
Emitter Only Theory,” the speed of light emitted is not increased by the speeder’s movement.
However, due to the speeder’s movement, the second photon had less distance to travel
before hitting the car. Therefore, the photons (pulses) were returned closer together than the
rate at which they were initially emitted.
Step 8: The police car is now a stationary observer waiting for the photons emitted by
the speeder’s vehicle. The receiver attached to the lidar gun receives first oncoming photon
emitted by the speeder’s car.
Step 9: The receiver attached to the lidar gun receives the second oncoming photon
emitted by the speeder’s car.
Step 10: The lidar gun calculates the difference between the times the two photons
were initially emitted and the time between the receipts of the two return pulses. It counts the
number of nanoseconds it took for the round trip of both pulses at the speed of light (186,282
miles per second). Since the distance light travels in a nanosecond (billionth of a second) is a
known distance, dividing the number of nanoseconds by 2 calculates the distance each pulse
traveled to the car. The difference in the time it took for pulse-1 to reach the speeder and
return and the time it took for pulse-2 to do the same thing provides the distance the speeder
traveled between pulses. By taking several hundred samples over the course of a third of a
second or so, the lidar gun can calculate the speed of the oncoming car, and the accuracy can
be very high. It calculates the speeder’s speed to be 90 mph.
In the above “experiment,” there was one moving observer involved – the speeder
while waiting for the arrival of the photons from the lidar gun. Due to his speed, the photons
arrived faster than the speed of light, disproving the “Mathematicians’ All Observers Theory.”
The police car was stationary when the lidar light was emitted, and although it was an
“observer” when the pulses were returned, the police car was stationary and thus not a
“moving observer.”
But what happens when the lidar gun is used from a police car that is moving at 60 mph
toward the speeder who is traveling at 90 mph?
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Figure 8
Step 1: The lidar gun is the still the emitter. The moving lidar gun in the moving police
car again emits very short pulses of laser light – a fraction of a second apart - toward the
speeder. As stated in “Einstein’s Emitter Only Theory,” the speed of the police car does not
affect the speed of light emitted. The speed of light will still travel at c, just as it did when the
police car was stationary. However, the police car will move a very short distance between the
emission of the first photon and the emission of the second photon.
Steps 2 through 7 are the same in this “experiment” as in the first “experiment.”
Step 8: The police car is now a moving observer waiting for the photons re-emitted by
the speeder’s vehicle. The receiver attached to the lidar gun receives the first oncoming
photon emitted by the speeder’s car. The photons arrive at c + v.
Step 9: The police car moves forward slightly while waiting for the arrival of the second
photon.
Step 10: The receiver attached to the lidar gun receives the second oncoming photon
emitted by the speeder’s car. Again, the photons arrive at c + v.
Step 11: The lidar gun again calculates the difference between the times the two pulses
were initially emitted and the time between the receipts of the two return pulses. The
difference in the amount of time between the two pulses was shortened by the movement of
the speeder just as in the first experiment. In the second experiment, however, the amount of
time between the two “reflected” pulses is further shortened by the movement of the police
car toward the second source of emission when the police car was a moving observer. The lidar
timing equipment assumes that all movement was done by the oncoming vehicle, and it will
register the oncoming vehicle’s speed as 150 mph.
If the “Mathematicians’ All Observers Theory” were valid, the lidar gun should have
registered zero mph, since that theory says that “the velocity of light in free space appears the
same to all observers regardless both of the motion of the source of light and of the
observer.”
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Radar guns and the Doppler Effect
Before there were any lidar guns, traffic control police cars had been using “radar guns”
to catch violators of speed laws since 1949.[14] The word “radar” was originally a U.S. Navy
abbreviation for “RAdio Detection And Ranging.”
The principles and steps are very straight forward and the same illustrations can be
used. I’ll just step through the “experiment” where only the speeder is moving:
Step 1: The radar gun in the stationary police car emits a pulse of radio waves of a
specific frequency per second toward an oncoming vehicle that is suspected of speeding.
Step 2: Because the oncoming vehicle is moving toward the police car, the radio waves
are received at a higher frequency than at which they were transmitted. The waves are “blue
shifted.” The wave lengths didn’t change, but more waves of the same length were received
per second than were emitted per second.
Step 3: The radio waves, arriving at c + v, are absorbed by atoms in the surface of the
oncoming vehicle at their incoming frequency.
Step 4: The atoms must immediately rid themselves of the excess energy, so they
immediately emit and radiate away new energy waves at the same frequency at which they
were received.
Step 5: Some of the new radio waves return to a receiver attached to the radar gun.
Step 6: The radar gun’s receiver measures the frequency of the new incoming waves
which, due to Doppler shifting, will arrive more frequently compared to the waves that were
transmitted by the same gun. The change in frequency (i.e., the “Doppler shift”) is used to
calculate the speed of the oncoming vehicle. The speeder’s speed is calculated to be 90 mph.
In the radar gun “experiment,” radio waves are emitted at one frequency by the radar
gun in the police car and then they are emitted at another frequency by atoms in the surface of
the speeding vehicle, and there is no actual measurement of the speed of the light waves
involved. It is assumed that the speed of light is constant.
Red and Blue Shifting
In astronomy, experiments and observations involving red and blue shifting of wave
lengths confirm “Einstein’s Emitter Only Theory” in that incoming light reaching a moving
observer in any observatory on Earth will be measured to arrive at the speed of light plus or
minus the speed of the observer.
If the observer is moving away from the source of the light, as appears to be the case
with the light from most stars in most galaxies in the visible universe, the light is said to be “red
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shifted.” It is understood that, in reality, the universe is expanding and therefore the stars and
galaxies are moving away from the Earth as the Earth moves away from them. Their movement
doesn’t affect the speed of light they emitted, but the Earth’s movement away from the stars
and galaxies does affect how observers on Earth will measure and view that light. Since the
Earth is moving away from the source of the light, the light will arrive at c – v, where v is the
Earth’s speed away from the source. This means the wave lengths of the light will appear
longer, i.e., shifted toward the red end of the visible spectrum.
Likewise, if the Earth is moving toward a star, the light from that star will arrive at c + v,
and the wave lengths will appear shorter than they really are, i.e., shifted toward the blue end
of the visible spectrum.
In 1887, Vogel and Scheiner discovered the “annual Doppler effect,” the yearly change
in the Doppler shift of stars located near the ecliptic due to the orbital velocity of the Earth.[12]
When the Earth is moving toward a star near the ecliptic, light from that star is blue-shifted
because more wave peaks reach the observer in a unit of time. When the Earth is moving away
from the star the light from the star is red-shifted because fewer wave peaks reach the
observer in a unit of time.
The wavelength defines the source of the light. If the light source is a sodium atom, for
example, the distance between the peak of one wave and the peak of the next wave should be
589.3 nanometers (nm). But if the observer is moving away from the light source, the distance
between one wave crest and the next will be greater than 589.3 nm by the distance the
observer traveled between the arrival of one wave crest and the next. The light will be red-
shifted. “Einstein’s Emitter Only Theory” works well with the known facts.
The “Mathematicians’ All Observers Theory,” however, argues that the observer will see
light arriving at the “universal speed of light” regardless of his own speed. Therefore, the
wavelength must somehow change if the observer is moving. The proponents of the theory
cannot explain how light changes frequencies to accommodate the observer, it is just described
as another one of those things about relativity that is “counter-intuitive.” I.e., it doesn’t work
the way common sense says it should work
Anomalies
It would appear that a proper understanding of “Einstein’s Emitter Only Theory” might
also explain the “mysterious” phenomena known as “flyby anomalies.” Flyby anomalies occur
when space probes are “sling-shot” past the Earth in order to gain additional velocity before
they head farther out into the solar system or into space beyond.
As with the Lunar Laser Ranging experiments, the “flyby anomalies” were instances
where light speed seems to combine with an observing object’s speed (an observatory on the
moving earth) to produce a velocity that appears greater than the speed of light. In the “flyby
16
anomalies,” space probes appeared to emit radio waves that moved faster than the speed of
light. There are also other “anomalies” where a space craft is moving away from the Earth and
signals from it arrive at a frequency that is lower than what the craft is known to have emitted.
Unfortunately, scientific papers about the anomalies do not provide information that
one could use as “evidence” showing that the changes in frequencies were caused by the
Earth’s movement toward or away from the moving object in space. One published paper[12]
argues that it must be the speed of the satellite (the emitter) that is being combined with the
speed of the radio waves it emits, even though many experiments show that to be an invalid
theory.
The “anomalies” are currently generally considered to be “unresolved.” But they may
have been resolved, since it seems no recent flyby missions have reported any “anomalies.”
The fact that regularly pulsing objects in space can disprove common misinterpretations
of the Second Postulate also brings pulsars to mind.
Pulsars
Pulsars are celestial objects thought to be a rapidly rotating neutron stars that emit
regular pulses of radio waves and other electromagnetic radiation at rates of up to one
thousand pulses per second. They can be viewed as being extremely accurate clocks in space
in that they typically pulse at a fixed rate for year after year.
So, we have a situation where the Earth is orbiting around the Sun at 30 kilometers per
second (19 miles per second), which means that at some point in the year (say December) the
Earth would be moving away from a pulsar at 30 kps, and six months later (in June) it would be
moving toward the pulsar at 30 kps.
Figure 9
If the motion of the independent observer has no effect on the measured speed of light,
the pulse rate measured in June should be the same as the pulse rate measured in December.
If the motion of the independent observer does affect the measured speed of light, then
light should be measured as arriving at 299,792 plus 30 kps when moving toward the pulsar and
at 299,792 minus 30 kps when moving away from the pulsar. Which means that, if the pulsar
pulses at exactly 100 pulses per second in September and March, it should pulse at 100.033
17
pulses per second if the Earth was moving toward the pulsar in June, and 99.9 pulses per
second if the Earth is moving away from the pulsar in December.
Unfortunately, it seems no one has done such measurements. Or, if they have, they
decided the results were wrong. Instead, measurements of the pulses from pulsars are
measured as if they were theoretically measured from the center of the Sun.
Conclusion
In a letter mailed from Prague in 1912 to his friend Paul Ehrenfest,[15] Einstein said this
of Ehrenfest: "You are one of the few theoreticians who has not been robbed of his common
sense by the mathematical contagion." He was referring to the mathematicians’ interpretation
of Relativity as if it were a disease. Einstein then goes on to explain how it took awhile for him
to realize that “the constancy of c exclusively for an observer sitting at the light source” was the
way light works. And he says, “I was convinced that all light is defined by frequency and
intensity alone, completely independent of whether it comes from a moving or resting source.
Further, it did not occur to me to consider that deflected radiation might behave differently
with regard to propagation from radiation newly emitted at the point in question.” But
gradually he realized he was wrong. He goes on to say, “All one can bring up in support of the
hypothesis of the independence of the velocity of light from the state of motion of the light
source is its simplicity and practicability.”
On January 27, 1921, Einstein began a lecture to the Prussian Academy of Sciences in
Berlin[4] with this comment: “One reason why mathematics enjoys special esteem, above all
other sciences, is that its laws are absolutely certain and indisputable, while those of all other
sciences are to some extent debatable and in constant danger of being overthrown by newly
discovered facts.” That sense of certainty seems to make mathematicians immovable in
arguments about Relativity.
A little research will find dozens of college professors repeating the “Mathematicians’
All Observers Theory” in on-line “study guides” and “lecture notes.” And, it is very often
accepted as an unquestionable fact, even though it means that if you have ten observers
traveling at different velocities toward a light emitting body, they will all somehow measure the
light as arriving at 299,792,458 meters per second. Those who interpret the Second Postulate
as working that way will argue that such a finding may seem “illogical,” but that is the nature of
Relativity, it is “non-intuitive.” Mostly they seem to argue that it is what Einstein wrote (which
it isn’t), and therefore it must be accepted – even if you think it is wrong.
It is wrong, it isn’t what Einstein wrote, and it shouldn’t have to be accepted.
18
References
[1] Einstein, A,: On the Electrodynamics of Moving Bodies, Annalen der Physik 17 (1905)
Translation by G. B. Jeffery and W. Perrett, The Principle of Relativity, London: Methuen and
Company, Ltd. (1923)
[2] Michelson, A. A., Morley, E. W.,: On the Relative Motion of the Earth and the Luminiferous
Ether, American Journal of Science 34 (1887)
[3] Einstein, A,: Quoted in Albert Einstein, Philosopher-Scientist, Open Court; 3rd edition
(December 30, 1998)
[4] Einstein, A,: Geometry and Experience, an address to the Prussian Academy of Sciences in
January 1921, published by Methuen & Co. Ltd, London (1922).
[5] Tolman, R. C.,: The Second Postulate of Relativity, Physics Review, Series I, XXXI (1) (1910)
[6] Serway, R. A., and Vuille,: C, College Physics – Ninth Edition, page 888, Brooks/Cole
(2012)
[7] Seeds, M. A., Backman,, D,: Foundations of Astronomy, Enhanced, Brooks Cole; 13th
edition, page 96 (January 1, 2015)
[8] Boden, M,: Primer of Relativity: A Student’s Introduction, Tafford Publishing; Student
Edition (November 8, 2006
[9] Cassidy, D. C., Holton, G., Rutherford, F. J.,: Understanding Physics, Springer, Chapter 9
(2002)
[10] Alväger, T., Farley, F. J. M., Kjellman, J., Wallin,L.,: Test of the second postulate of special
relativity in the GeV region, Physics Letters (October 1, 1964)
[11] Aleksandrov, E. B., Aleksandrov, P. A., Zapasskii, V. S, Korchuganov, V. N., Stirin, A. I.,:
Measuring Speed of the Light Emitted by an Ultrarelativistic Source, JETP Letters (2011
[12] Pannekoek, A,: A History of Astronomy. Dover, p. 451. ISBN 0-486-65994-1. (1961)
[13] Gezari, D. Y.,: Lunar Laser Ranging Test of the Invariance of c, arxiv.org (2010)
https://arxiv.org/abs/0912.3934
[14] The New York Times. 8 February 1949
[15] Beck, A (translator),: English Translation of The Collected Papers of Albert Einstein, Vol. 5:
The Swiss Years: Correspondence, 1902–1914, Princeton University Press (1995).